What are the divisors of 179?

1, 179

There is a total of 2 positive divisors.
The sum of these divisors is 180.
The arithmetic mean is 90.

2 odd divisors

1, 179

How to compute the divisors of 179?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 179 by each of the numbers from 1 to 179 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

179 / 1 = 179 (the remainder is 0, so 1 is a divisor of 179)
179 / 2 = 89.5 (the remainder is 1, so 2 is not a divisor of 179)
179 / 3 = 59.666666666667 (the remainder is 2, so 3 is not a divisor of 179)
...
179 / 178 = 1.0056179775281 (the remainder is 1, so 178 is not a divisor of 179)
179 / 179 = 1 (the remainder is 0, so 179 is a divisor of 179)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 179 (i.e. 13.37908816026). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

179 / 1 = 179 (the remainder is 0, so 1 and 179 are divisors of 179)
179 / 2 = 89.5 (the remainder is 1, so 2 is not a divisor of 179)
179 / 3 = 59.666666666667 (the remainder is 2, so 3 is not a divisor of 179)
...
179 / 12 = 14.916666666667 (the remainder is 11, so 12 is not a divisor of 179)
179 / 13 = 13.769230769231 (the remainder is 10, so 13 is not a divisor of 179)